Calculation of the sodium vacancy thermal coefficient of expansion

The method of lattice statics is used to calculate the temperature variation of the vacancy formation volume $\Delta V$ of sodium in the range 90-300 K. $\Delta V$ is shown to derive its temperature dependence from that of the elastic constants and that of the interionic potential taken from the work of Rasolt and Taylor. The thermal coefficient of expansion of the sodium vacancy is found to be about 15 times greater than that of the perfect lattice at high temperature. This result could play an important role in high-temperature defect measurements and provides at least a partial explanation for the Arrhenius-plot curvature in sodium.